The imaging and inspection of extreme ultraviolet (EUV) masks is an important aspect of EUV lithography. The availability of actinic mask inspection tools able to generate highly resolved defect maps of defective EUV layouts is needed to ensure defect-free wafer prints. The technological interest towards phase-shift absorber materials for the next generation of EUV masks, and the associated need for phase metrology at the absorber level, makes phase retrieval methods a particularly interesting option for actinic inspection. In this work we use ptychography as an inspection tool for EUV masks. We show how variational and statistical methods can be employed to include a-priori information in the ptychographic inverse problem and how to cluster different update rules - stemming from the minimization of appropriate cost functionals - to optimally include prior information in ptychography under Poisson noise.